Response-dependence theses are usually formulated in terms of a priori true biconditionals of roughly the form ‘something, x, falls under the concept ‘F’ ↔ x would elicit response R from subjects S under conditions C’. Such formulations are vulnerable to conditional fallacy problems; counterexamples threaten whenever the C-conditions’ coming to obtain might alter the object with respect to F. Crispin Wright has suggested that such problems can be avoided by placing the C-conditions in a proviso. This ensures that any changes triggered by the C-conditions’ coming to obtain will be irrelevant to the truth of the biconditional. I argue that this move leaves the equations vulnerable to counterexamples of a slightly different kind: Cases where the change is triggered, not by the C-conditions’ coming to obtain, but by the response. I consider two ways to resist these counterexamples, and argue that both are insufficient. The upshot is a challenge that must be met if provisoed biconditionals are to serve their purpose.